Properties

 Label 139650.ja Number of curves $2$ Conductor $139650$ CM no Rank $0$ Graph Related objects

Show commands: SageMath
sage: E = EllipticCurve("ja1")

sage: E.isogeny_class()

Elliptic curves in class 139650.ja

sage: E.isogeny_class().curves

LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
139650.ja1 139650cj2 $$[1, 0, 0, -19843188, 34020853992]$$ $$-470056203380406889/1296351000$$ $$-2383037481234375000$$ $$[]$$ $$10450944$$ $$2.7592$$
139650.ja2 139650cj1 $$[1, 0, 0, -163563, 78131367]$$ $$-263251475929/1282741110$$ $$-2358018888287343750$$ $$[]$$ $$3483648$$ $$2.2099$$ $$\Gamma_0(N)$$-optimal

Rank

sage: E.rank()

The elliptic curves in class 139650.ja have rank $$0$$.

Complex multiplication

The elliptic curves in class 139650.ja do not have complex multiplication.

Modular form 139650.2.a.ja

sage: E.q_eigenform(10)

$$q + q^{2} + q^{3} + q^{4} + q^{6} + q^{8} + q^{9} + 3 q^{11} + q^{12} + 5 q^{13} + q^{16} + q^{18} - q^{19} + O(q^{20})$$ Isogeny matrix

sage: E.isogeny_class().matrix()

The $$i,j$$ entry is the smallest degree of a cyclic isogeny between the $$i$$-th and $$j$$-th curve in the isogeny class, in the LMFDB numbering.

$$\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)$$

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)

The vertices are labelled with LMFDB labels. 